Resonant Scattering and Glass Transition (JJAP)
A paper submitted to the JJAP on elastic resonance of particles in liquids has been accepted for publication.
Our laboratory studies the properties of nano or micron particles in liquids using ultrasonic waves, where the mechanical information is in contrast. We have produced three major techniques: a technique to evaluate particle size from their motion (DSS method), a technique to evaluate particle rigidity (US method), and a technique to characterize the surface charge condition of particles (ESS method). In particular, the DSS and ESS methods are our original technologies, which have no other similar techniques. In this study, we used the US method to investigate the bulk elasticity of droplets suspended in a liquid and the rigidity of solid particles in a non-contact way.
When a polymer solution (e.g., a toluene solution of polystyrene) is emulsified in water, droplets consisting mainly of an organic solvent and a polymer are dispersed in the water to form an emulsion. Evaporation of the solvent from these droplets should eventually result in solid particles. We have stated that it is possible to know to what extent the droplet is liquid or solid up to the point of concentration by the method shown in the previous paper. The rigidity of these droplets or solid particles dispersed in water can also be determined by ultrasonic waves without contacting them directly. In this study, we focused on polymers of various materials and investigated their ultrasonic properties during the drying process. Some of these polymers are glassy solids when the solvent is completely dry, while others remain in a liquid state. The objective of this study was to determine the shear modulus, a property of solids, as a function of glass transition temperature for these polymer particles. The polymers that comprise the particles initiate thermal motion of their main chains at the glass transition temperature. Therefore, the glass transition has been investigated in connection with viscosity. Since the shear modulus is a property of solids, it corresponds to properties at much lower temperatures than the glass transition temperature. No study has ever dealt with this at the level of small particles.
In general, elasticity or rigidity ranges from bulk elasticity, which is the resistance of water to compression, to shear elasticity, which is the resistance of a solid to shear deformation, and so on. The contribution of compression is largely reflected in the longitudinal elastic modulus and the ultrasonic waves almost exclusively reflect the contribution of compressional elasticity. On the other hand, the shear modulus is much smaller than the bulk modulus, making it very difficult to evaluate the shear modulus of particles in water, even with ultrasound, which has the advantage of non-contact analysis. In the field of ultrasonic scattering, there were two theories, one by Epstein and Carhart that considered the shear viscosity of droplets and the other by Allegra and Hawley that considered the shear modulus of solid particles. Together, these are often referred to as the ECAH theory and can be used to evaluate viscosity and elasticity. However, the EC model is used for droplets dispersed in water and the AH model for solid particles dispersed in water, and the case where particles are both viscous and elastic at the same time has not been studied. This is because one considers velocity balancing in the case of liquids and displacement balancing in the case of solids at the liquid-particle interface. We have generalized this concept to the viscoelastic ECAH analysis, which allows us to analyze the entire process of transition from a droplet to a solid. During this transition, it is possible to quantitatively analyze the state in which the particle contains both viscous loss and storage elasticity.
In addition, the ultrasonic spectroscopy (US) method has a very large number of sample properties that need to be known in advance, making it difficult to easily determine shear elasticity and shear viscosity. In this study, we also described a method to easily determine the modulus of elasticity, although it is for micron-sized particles (Appendix of the paper). This paper was written for a special issue of the Ultrasonic Society of Japan, a peer-reviewed English-language journal. If you are interested in particle modulus analysis, which studies resonant scattering of particles dispersed in water, please take a look at the paper.